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The Framework for Developing Parameterizations

Throughout the workshop, participants discussed the purpose of model parameterizations as well as the methods and means of developing and testing them. These discussions broached subjects such as fundamental challenges of modeling component processes, problems with tuning model parameterizations as opposed to fully evaluating them, field programs to test and improve parameterizations, and the use of community models to develop and test complex dynamical systems.

UNDERSTANDING AND PARAMETERIZATION

The unattractiveness of the word “parameterization”1 may betray a sense of imperfection that surrounds the concept. Perhaps it is regarded by some as an unsatisfactory fix awaiting the day when the process in question can be explicitly simulated. But parameterizations serve two

1  

Parameterization is defined by the American Meteorological Society (2000) as “The representation, in a dynamic model, of physical effects in terms of admittedly oversimplified parameters, rather than realistically requiring such effects to be consequences of the dynamics of the system.” An alternative definition appears in the summary section of this report (see Chapter 5).



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Improving the Scientific Foundation for Atmosphere-Land-Ocean Simulations: Report of A Workshop 3 The Framework for Developing Parameterizations Throughout the workshop, participants discussed the purpose of model parameterizations as well as the methods and means of developing and testing them. These discussions broached subjects such as fundamental challenges of modeling component processes, problems with tuning model parameterizations as opposed to fully evaluating them, field programs to test and improve parameterizations, and the use of community models to develop and test complex dynamical systems. UNDERSTANDING AND PARAMETERIZATION The unattractiveness of the word “parameterization”1 may betray a sense of imperfection that surrounds the concept. Perhaps it is regarded by some as an unsatisfactory fix awaiting the day when the process in question can be explicitly simulated. But parameterizations serve two 1   Parameterization is defined by the American Meteorological Society (2000) as “The representation, in a dynamic model, of physical effects in terms of admittedly oversimplified parameters, rather than realistically requiring such effects to be consequences of the dynamics of the system.” An alternative definition appears in the summary section of this report (see Chapter 5).

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Improving the Scientific Foundation for Atmosphere-Land-Ocean Simulations: Report of A Workshop purposes. From a practical point of view, they enable predictions and/or simulations; that is, they are a means to an end. In addition, however, parameterizations encapsulate our understanding of the physical interactions among disparate scales and processes. From this point of view, parameterizations are a route to understanding. It is a truism of dynamical systems theory that simple component processes can combine in a coupled nonlinear system to yield unexpected emergent behaviors, through feedback among the components. The computational simulation models in wide current usage would seem rife with such possibilities, yet they usually are configured to maximize stability and minimize surprises. This is partly due to a prudent conservatism, but it does avoid the central issue of unexpected emergent behaviors. Because the large models can only have a small portion of their possible behaviors explored, an essential companion activity is discovering and fully understanding a suite of artfully conceived, elegant, minimally constructed models of canonical emergent behaviors germane to the atmosphere and ocean. Some examples of such elegant models are low-order geochemical box (i.e., well-mixed reservoir) models and oscillator models for El Niño-Southern Oscillation and paleoclimatic cycles, as well as more fluid-dynamical models for turbulent boundary layers, synoptic weather life cycles, and the turbulent equilibrium of a zonal baroclinic jet. Many more canonical models for relevant emergent behaviors are needed if our field is ever to come to trust and understand the abundant but complicated evidence from simulation models and measurements. It is possible to conceive of a purely empirical route to parameterization in which understanding is only required at the level of asserting that the process can be represented in terms of large-scale variables and identifying which of those variables the process in question should depend on. The specific relationship between these variables and the process would be determined purely by experiment. Although such an empirical method may be possible, it would no doubt prove cumbersome. Moreover, not adequately understanding the physical processes would make it less robust, and it likely would be less satisfying intellectually. This highlights the intimate connection between understanding and parameterization, which can be regarded as an embodiment of a set of physical hypotheses. The most satisfying parameterizations start out with an understanding of the importance of the process to be parameterized, followed by an elegant hypothesis about the relationship

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Improving the Scientific Foundation for Atmosphere-Land-Ocean Simulations: Report of A Workshop between the process in question and the explicitly simulated variables, and concluding with the subjecting of that hypothesis to rigorous experimental evaluation. To the extent that the parameterization succeeds, it also serves to validate our understanding of the process. In this sense the process of finding an ideal parameterization is intimately connected with our quest to understand nature. At the heart of this endeavor lies the notion of elegance (see Appendix C for Isaac Held’s paper describing this concept), which encompasses clarity and simplicity, coupled with explanatory and predictive power. Progress in developing better representations of physical, chemical, and biological processes will depend in part on conveying to prospective students and researchers the true relationship between such development and the quest for understanding nature. TUNING VERSUS EVALUATION A parameterization may be thought of as an embodiment of a set of physical hypotheses. As such, confidence in its performance must be based on rigorous tests against observations and/or direct or large-eddy simulations. Parameterizations are typically based in part on simplified physical models (e.g., entraining plume models in convection schemes). The parameterizations also involve numerical parameters that must be specified as input. Some of these parameters can be measured, at least in principle, while others cannot. The introduction of parameters that cannot be measured even in principle needs to be avoided, but in our current state of ignorance it is sometimes unavoidable. The assigned values of unmeasurable parameters are always chosen to optimize the realism of model results, but this may introduce compensating errors. Obviously, parameters that can be measured should be set to their measured values. But even here, experience shows that in some cases model results can be improved by departing from the measured values (i.e., by using incorrect values of the parameters). In such cases the errors introduced by the incorrect parameter values are presumably compensating for other, unknown errors in the model. The use of demonstrably incorrect parameter values was considered by some workshop participants as an egregious kind of tuning.

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Improving the Scientific Foundation for Atmosphere-Land-Ocean Simulations: Report of A Workshop Observational tests of parameterizations can be divided into two types. First, there are direct tests of the parameterizations or the physical assumptions that underlie them. The second type of test consists of running a model that uses the parameterization and evaluating the results of the model against observations. Tests of the first type are more fundamental. Perhaps a good example of this first type of test is the development, testing, and refinement of parameterizations of surface fluxes over the ocean. The early formulations, based strictly on dimensional reasoning, were subjected to rigorous tests in the field and in laboratory experiments. These experiments determined certain universal constants within reasonable bounds and pointed to systematic deficiencies in the early formulations. Based on these results, the formulations were refined and further experimental tests were made. Today, except perhaps at very high and very low wind speeds, these formulations are used in large-scale simulations with a high degree of confidence, and the constants that appear in the surface-flux formulations are not usually considered tunable parameters. By contrast, the development and testing of convective parameterizations have proceeded along a different route, leading to the present circumstance in which many different schemes are in use and there is no general agreement on what constitutes a superior scheme. This different route is at least partially due to the fact that testing convective schemes in the field is very difficult compared to, say, testing surface-flux parameterizations. A methodology has been devised whereby rawinsonde arrays are used to measure horizontal and vertical advection, and surface-based and satellite-borne radiometers measure radiative fluxes. These fluxes, together with estimates of surface fluxes, are used to drive single-column models in which the only truly free process is the convection, which is parameterized. Integration of the single-column model over a reasonable period of time will result in large errors in quantities such as relative humidity, unless the convective fluxes are accurate. Field programs that are being carried out using this methodology include the GEWEX (Global Energy and Water Vapor Experiment) Cloud Systems Study (GCSS) (Randall et al., 2003) and the Atmospheric Radiation Measurements (ARM) program of the U.S. Department of Energy (Morcrette, 2002). Typically, field data are integrated to provide a comprehensive case study, which also is simulated by high-resolution numerical models. The observations are

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Improving the Scientific Foundation for Atmosphere-Land-Ocean Simulations: Report of A Workshop used to evaluate the high-resolution model results, and both are used to evaluate the parameterizations. The first experiments designed specifically to enable parameterization tests of this type occurred during the 1990s. Recent and near-future examples include the Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) experiment (Stevens et al., 2003), the Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL FACE) (Jensen et al., 2004), the Rain in Cumulus over the Ocean (RICO) experiment (http://www.ofps.ucar.edu/rico/), and ARM’s Tropical Warm Pool International Cloud Experiment (TWP-ICE) (May et al., 2004). Such evaluations have revealed that cloud system resolving models, forced the same way, produce systematically better results than convective parameterizations. At the same time, few convective schemes in current use have been subjected to such rigorous tests. Often, a new scheme is simply inserted into a large-scale model and evaluated based on the overall performance of the model. This is usually an ill-posed enterprise, however, because model error generally arises from many components. Workshop participants stressed the need to test physical representations as far as feasible against observations or, especially where observations are lacking, against direct numerical or large-eddy simulations of the process in question. Parameterizations can now also be tested against detailed numerical simulations of the process. Both large-eddy simulation (LES) and the exact but low Reynolds number form called direct numerical simulation (DNS) have been used in this way to complement and extend what can be done through direct observations. Because many processes must be parameterized in atmosphere-land-ocean models (A-L-O), and because they can strongly influence model fidelity, it is important that their parameterizations be developed and tested in this way to the extent possible. COMMUNITY MODELS AS A FRAMEWORK FOR DEVELOPING AND TESTING PARAMETERIZATIONS Complex dynamical-system computational models are essential tools for the science of weather analysis and forecasting, small-scale geophysical fluid dynamics, climate, oceanic circulation, and biogeochemical cycling in Earth’s system. They have come to have such com-

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Improving the Scientific Foundation for Atmosphere-Land-Ocean Simulations: Report of A Workshop plexity in their functional breadth and computational technology that they must be developed, maintained, used, tested, evolved, and managed by ever larger and more diverse groups of scientists. National laboratories manage much of the communal modeling activity. Yet modeling practices could be more productive if the relationships of these laboratories with non-laboratory modeling scientists were strongly collaborative because a wealth of intelligence and labor exists outside laboratories (e.g., at universities, within the private sector). Although this principle is widely acknowledged, its practical implementations are still rudimentary. In all cases, community models are applied by a community of users. Here “community” is understood to mean a multi-institutional group. Although the creation and support of a community model can be a huge and difficult task, it is relatively easy to induce a community of users to make applications of a well-constructed and well-supported community model. In some cases, community models are also developed by a community. This is much more difficult to accomplish, for a variety of reasons. One is that, empirically, there are fewer people with the inclination or ability to do model development than there are model users. A second factor is that virtually all community models are identified with one primary or host institution, and the staff of the host institution inevitably feel some ownership of the model. As a result, outsiders who want to participate in model development may find that they need a collaborator on the inside of the host institution. Moreover, there are logistical and infrastructure issues that serve as a barrier to outsiders, including the technical difficulty of interfacing new code with a complex model that has complex data structures, testing the code, and then debugging it. Because it usually is faster and more effective to interact with the core model staff in person, an extended visit to the host institution may be required. The continued development of an established community model needs to be carried out very carefully. It is important that the model which can be thought of as the “crown jewels”not be broken. As a result, established community models tend to evolve slowly and conservatively. For example, the recent new release of the Community Atmosphere Model (CAM), which is the atmospheric component of the Community Climate System Model (CCSM), is not very different from the preceding version. The legacy of the CAM can be traced back more than 20 years. Interestingly, some of the newer, less established

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Improving the Scientific Foundation for Atmosphere-Land-Ocean Simulations: Report of A Workshop components of the CCSM (e.g., sea ice, land-surface processes, biogeochemistry) have undergone much more rapid recent development.